Im currently running a stepper motor and 6 DC Motors. The stepper motor is continuously on and running from a 12v power supply via the VIN pin and the DC Motors are only triggered one at a time from the 5V pin. However, when the DC Motors are turned on (via a microswitch), the Stepper motor stalls for about 3 seconds then starts again. The DC Motor does not loose power. When the DC Motor is turned on, causing the stalling of the stepper, the L, TX and RX LEDs flash on the Arduino board (Uno).

Is something shorting/back currenting and the Arduino protecting itself by resetting? Do I need to use capacitors or diodes anywhere to prevent this, if so, where in the circuit?

It definitely sounds like your Arduino is resetting due to the surge in current caused by turning a DC motor on. It's tough to figure out exactly what's going on without some kind of diagram showing how you've got things hooked up.